Related papers: Rotation-Invariant Spherical Watermarking via Thir…
This paper develops the theory behind the bispectrum, a concept that is well established in statistical signal processing but not, until recently, extended to computer vision as a source of frequency-domain invariants. Recent papers on…
Accurate 3D volumetric mapping is critical for autonomous underwater vehicles operating in obstacle-rich environments. Vision-based perception provides high-resolution data but fails in turbid conditions, while sonar is robust to lighting…
We present and implement an algorithm for computing the invariant circle and the corresponding stable manifolds for 2-dimensional maps. The algorithm is based on the parameterization method, and it is backed up by an a-posteriori theorem…
We consider $\mathbb{R}^3$ as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary $\tau\in \widehat{SO(3)}$, let $E_\tau$ be the homogeneous vector bundle over $\mathbb{R}^3$…
Recent work by McClarren & Hauck [29] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the…
Analyzing volumetric data with rotational invariance or equivariance is an active topic in current research. Existing deep-learning approaches utilize either group convolutional networks limited to discrete rotations or steerable…
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…
Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making…
We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding…
Recent work has achieved dense 3D reconstruction with wide-aperture imaging sonar using a stereo pair of orthogonally oriented sonars. This allows each sonar to observe a spatial dimension that the other is missing, without requiring any…
The quantum rotor is shown to be supersymmetric. The supercharge $Q$, whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that commute with $Q$ form the algebra $so(3)_{-1}$, an…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical…
We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…
We investigate the topological phase associated with the double connectedness of the SO(3) representation in terms of maximally entangled states. An experimental demonstration is provided in the context of polarization and spatial mode…
While the proposal of the Tri-plane representation has advanced the development of the 3D-aware image generative models, problems rooted in its inherent structure, such as multi-face artifacts caused by sharing the same features in…
We consider a class of third-order evolution equations of the form \begin{equation*} \left\{ \begin{array}{l} \displaystyle u_{t}=F\left(x,t,u,u_x,u_{xx},u_{xxx},v,v_x,v_{xx},v_{xxx}\right), \displaystyle…
Given a single RGB panorama, the goal of 3D layout reconstruction is to estimate the room layout by predicting the corners, floor boundary, and ceiling boundary. A common approach has been to use standard convolutional networks to predict…
Watermarking methods have always been effective means of protecting intellectual property, yet they face significant challenges. Although existing deep learning-based watermarking systems can hide watermarks in images with minimal impact on…
3D Large Vision-Language Models (3D LVLMs) built upon Large Language Models (LLMs) have achieved remarkable progress across various multimodal tasks. However, their inherited position-dependent modeling mechanism, Rotary Position Embedding…